Lucky Number Premium: Numerological Superstition and Irrational ...

[Pages:34]Lucky Number Premium: Numerological Superstition and Irrational Valuation on the Stock Market

Pei-Shih Weng National Dong Hwa University, Taiwan

Yu-Wen Huang National Dong Hwa University, Taiwan

Abstract

This study shows that the firms with lucky listing codes on the Taiwan Stock market are traded at a premium compared to the firms with unlucky listing codes. The lucky number premium exists without interruption until the 44th month after IPO, and can still be found in the long run--at least nine years after IPO. We believe that this long-lasting premium for firms with lucky listing codes just represents investors' irrational preference for lucky numbers. This phenomenon can be viewed as evidence that cultural numerological superstition induces behavioral biases on the stock market. Further examination shows that the digits. 8 and 9 are particularly favored by investors. The lucky number premium is robust in different sub-periods from the 1990s to 2008, but has vanished in recent years. Interestingly, the lucky number premium only appears for firms with a low institutional holding, implying that individual investors are more likely to be affected by numerological superstition.

Keywords: Value Premium, Numerological Superstition, Behavioral Bias

Corresponding author. Pei-Shih Weng is Assistant Professor at the Department of Finance, National Dong Hwa University. Mail addressing: C309, College of Management, No.1, Sec.2, Da Hsueh Rd., Shou-Feng, Hualien 974, Taiwan; Email: psweng@gms.ndhu.edu.tw; Tel/Fax: +886-3-863-3148.

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1. Introduction

In the last few decades there has been a tremendous wave of interest in Behavioral Finance. Daniel Kahneman was awarded the 2002 Nobel Memorial Prize in Economic Sciences for having integrated insights from psychological research into economic science, and this has inspired more researchers to study human judgment and decision-making under uncertainty from the viewpoint of behavioral biases.1 Since 2002, psychology has become more and more influential in financial research, and particularly in explaining individual trading behavior. For instance, Barber, Lee, Liu, and Odean (2009) investigate how much an individual investor will lose in his or her trading, and note that, during 1995 to 1999, on average, individual investors in Taiwan lost about 187 million New Taiwan Dollar annually, which is about 2% of the GDP of Taiwan in the same period. Barber et al. (2009) attribute the dramatic losses of individual investors to the fact that investors in the Taiwan stock market, especially individual investors, often show irrational investment behavior and view their investments as a gamble. Similarly, Han, Lee, and Liu (2009) find that individual investors tend to perform poorly in the Taiwan option market. They argue that the disposition effect, a well-known behavioral bias explained by prospect theory, seriously distracts individual investors in their trading performance.2

Among the various kinds of behavioral biases, cultural superstition, which represents an

1 2 The theory was put forward in 1979 and developed in 1992 by Daniel Kahneman and Amos Tversky as a psychologically more accurate description of decision making than the expected utility theory. Their paper "Prospect Theory: An Analysis of Decision under Risk" (1979) has been called a "seminal paper in behavioral economics".

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example of an affect heuristic, can frequently be observed in our daily life. In western superstition, for instance, Friday 13th is considered an unlucky day. According to the Stress Management Center and Phobia Institute in Asheville, North Carolina, an estimated 17 to 21 million people in the United States are affected by a fear of this day, making it the most feared day and date in history.3 Some people are so paralyzed by fear that they avoid their normal routines in doing business, taking flights or even getting out of bed. Chinese superstition is similar, and although most people no longer have deep roots in traditional thinking, they are still susceptible to the culture, and behave accordingly. For instance, many people who are affected by Chinese culture believe in Feng Shui, a Chinese philosophical system according to which people should be concerned about the intangible influences of nature when they choose where they are to live or be buried, to avoid misfortune, even though there is no natural process linking the two events.4 When the idea that Feng Shui causes bad luck is prevalent, people think that "it is better to believe that it exists than to believe that it does not", instead of relying on scientific evidence.

Numerological superstition is also a well-known superstition in Chinese culture. People believe that some numbers can be classified as "lucky" or "unlucky". For instance, Thompson gave the following classification and explanation (1996, p.71) "Six" sounds similar to the word

3 This information is retrieved from John Roach "Friday the 13th Phobia Rooted in Ancient History". National Geographic News, 12 August 2004. The news is available at 4 A more detailed description of Feng Shui can be found at

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for "wealth", making it an extremely popular number; 2) "Eight" sounds like the word for "multiply" and represents good luck, and so eight is considered to be a "fertile number"; 3) "Nine" is considered one of the luckiest numbers because it sounds like the word for "longevity" and "long life"; and 4) "Four" sounds like the word for "death" and is considered very unlucky unless it is combined with a favorable number. The superstition about numbers is also found in people's manners in Taiwan, because of the social and cultural commonality between Taiwan and mainland China. For example, in Taiwan, when people purchase real estate, they sometimes try to avoid an address that contains the number "four" or is on the fourth floor; some hotels or hospitals also avoid the fourth floor, and name the floor above the third floor as the fifth floor. A similar phenomenon can be seen in Singapore. In the movie "Rogue Trader", for example, the leading actor Nick Leeson accepts the recommendation of a local employee in Singapore (who said to him that "eight" is a lucky number) and creates an account with the number "88888" in order to cover up his investment losses. Since the influence of cultural superstition is so effective in individual behavior and decisions, would numerological superstition, for example, also affect investors? This question motivates our analysis.

In this paper, we focus on the irrational influence, if any, of the numerological superstition of market investors on the value of public companies on the Taiwan Stock Exchange (TWSE). We hypothesize that the preference for specific numbers should affect the stock selection made by investors. Since each listed company on the TWSE has a unique 4-digit code as its trading

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symbol, companies with listing codes containing lucky digits such as 6, 8, or 9 should be favored by investors over companies with unlucky listing codes. Using Tobin's q, a proxy measuring the equity value, we examine the existence of a "lucky number premium", being the difference between the equity value of companies with a lucky listing code and that of companies with an unlucky listing code.

More specifically, our study consists of the following steps of analysis: 1. We examine thoroughly whether investors on the TWSE are numerologically

superstitious. If investors believe that investing in a firm with a lucky listing code will bring them fortune in their investment, such firms should enjoy a "lucky number premium" in terms of a higher equity value. 2. Having been able to show the existence of a numerological superstition in relation to investments on the TWSE, we further investigate whether the value premium for this behavior will be resolved in the short-run or will last for the long term. Also, we study whether the numerological superstition occurs in specific periods or is a constant phenomenon across different time periods. 3. We examine whether individual trading is the main cause of the lucky number premium.

Our empirical results are briefly summarized as follows. First, we find that, on the TWSE, those companies with a listing code containing lucky digits tend to be traded at a distinct value

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premium over those firms with a listing code containing an unlucky digit. Further examination shows that 8 and 9 are particularly favored by investors. Second, the lucky number premium exists without interruption until the 44th month after IPO, and can still be found in the long run--at least nine years after IPO. We believe that such a long-lasting premium for firms with lucky listing codes just represents investors' significant preference for lucky numbers. The phenomenon can also be viewed as evidence that cultural numerological superstition induces irrational investment preferences. Third, the lucky number premium is robust in different subperiods from the 1990s to 2008, but has vanished in recent years. Finally, the lucky number premium is only seen for those firms with a low institutional holding, implying that individual investors are more likely to be affected by numerological superstition and to cause the lucky number premium on the TWSE.

The rest of this paper is structured as follows: Section 2 briefly reviews the prior literature, addressing both the empirical and the theoretical aspects of superstition and behavioral bias in investments. Section 3 describes the data and the methodology. Section 4 presents the empirical findings and Section 5 concludes the study.

2. Literature Review

In this section, we briefly review the relevant prior literature. In the first subsection, we discuss investors' behavioral biases in general, as presented in previous studies; investors' superstitions that have been examined in the literature are specifically introduced in the next

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subsection.

2.1 Behavioral Bias

Several studies have noted that the irrationality of investors seems to be closely connected to investor sentiment and then to be reflected in stock price performance. Hirshleifer and Shumway (2003) find that from 1982 to 1997, across twenty-six countries, daily stock returns are affected to a large extent by morning sunshine. More specifically, sunshine affects the emotion, and investors are more optimistic when they are in a good mood than when they are in a bad mood, thereby affecting stock market performance. Kamstra, Kramer, and Levi (2003) investigate the role of seasonal affective disorder (SAD) in the seasonal time-variation of stock market returns, and find that the season affects investors' risk preferences and investment behavior. In the Taiwan market, Tsai, Wang and Chang (2009) employ principal component analysis to form a composite index of sentiment (including market turnover, the number of IPOs, the returns on IPOs, and the equity share in new issues) and show that the portfolio returns when investor sentiment is high are higher than when investor sentiment is low. From the studies discussed above, we can speculate that when an investor is undergoing emotional instability, his or her investment decisions will be affected.

2.2 Superstition

Early psychological theorization on superstitious beliefs can be traced back to Darke and Freedman (1997), who found that the causes of belief in good luck are closely related to feeling

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fortunate or generally satisfied with one's life. Superstitious beliefs have also been considered in relation to investors indirectly. Jiang, Cho and Adaval (2009) find that if Asian consumers are subliminally primed with luck-related concepts, it makes them feel luckier. Similar examples abound in the literature. Heath, Huddart and Lang (1999) examine the relationship between psychological factors and the exercise of stock options, to investigate how 50,000 employees at seven corporations decide to exercise their stock options. The authors find that exercise during the preceding month is positively related to stocks; in contrast, over a longer period, exercise is negatively related to returns. These results are consistent with psychological models of beliefs.

There have been a number of studies that have investigated how numerological superstitions affect trading. Bhattacharya, Kuo, Lin and Zhao (2014) find that, on the Taiwan Futures Exchange, individual investors submit disproportionately more limit order's price at "8" than at "4". The study also points out that the main reason for losses suffered by individual investors is numerological superstition. Haggard (2015) examines the stock return impact of days with "lucky" numbers in markets dominated by Chinese participants, and demonstrates a "lucky" number date trading strategy for the Shenzhen market that produces risk-adjusted returns in excess of the market return. Hirshleifer, Jian, and Zhang (2014) show that the frequency of lucky numerical stock listing codes exceeds what would be expected by probability, due to superstition effects; and that firms with "lucky" number listing codes initially

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